This is more my opinion on what to look for, rather than a specific recommendation. The only reason I've been on this forum for the past 17 years is to find or modify headlamps for the purpose of trail running or similar activities. I live far enough north that I run in the dark for months every year.
I agree you on the importance of having good flood for side illumination so you aren't running in a tunnel, but just as importantly to light up the ground at your feet so you don't trip over roots and rocks. I also like good throw to see where I'm going (more important on trails that are unmarked, or off trail in the woods) and to pick up animals like bears and moose with a safe margin to react. A completely smooth light experience is also important, without shadows or noticeable transitions, or any place where you are burning a hole in the ground, which would be wasteful and make the rest of the beam look not bright enough. I want a smooth, wide carpet of light from my feet to the range of the light.
I'd sacrifice range before flood, but to get that smooth carpet of light out to the range that I want, I need around 300 lumens minimum for something like a backup/emergency light. I prefer a sustainable 500-600 lumens as a medium level and 1000+ lumens on high. To get that much light for the 2 hours I generally need, that means 18650 lights. I know kreisl's opinion, "
imho "no 18650 headlamp is really recommendable for jogging" (©2020 kreisl)", but as a trail runner light geek, I have settled into a 2x18650. 1x18650 is enough for a backup kind of light, and 1x21700 contains enough energy for what I need, but I'm using an inexpensive system that uses the typical 2x18650 bike light battery pack, and that's good enough for me. Plus, headlamp season is cold season for me, so 2x18650 provides a good margin to counter diminished capacity in sub-freezing temperatures.
Balance is a lot more important than weight in a headlamp for running. My headlamp is 232 gram total weight, including the 2x18650 battery pack. It's more comfortable and has less bounce than my 3xAAA Princton Tec Eos that weighed around 100 g complete, but was front heavy. Weight on the head is more important for cycling than running because of the forward lean meaning your neck is holding your head cantilevered out there, yet night mountain bikers typically wear not only a helmet, but a headlamp and maybe 2x18650 battery pack on that helmet. You hear of long distance cyclists with neck issues, but not ultrarunners - so weight by itself is just not an issue for running. My headlamp is comfortable enough that I put it on at home even if I'm starting a run an hour before sunset, and I don't necessarily take it off after the run if I'm running errands. I don't really notice it's there - it's just comfortable. And no, I don't really care if it's pocketable. It's not a EDC device the way I use headlamps. I put it on as a tool to use for night running illumination.
Here's my current light. It's an old Yinding with neutral white XM-L2s (light head weight 59 g on the front) that was popular with the mtbr lights and night riding forum. This light has been measured at around 1200 lumens OTF on high by mtbr forum people, which is a sustainable output when running in the cold. I typically use it on medium (roughly 600 lumens) to ensure sufficient runtime, and that's sustainable at any temperature that I run in during headlamp season. I switched out one of the ~15 degree (half width) spot TIRs with a 45 degree (not sure half or full width) floody TIR. The headstrap is trimmed down to the minimum, including not using the rear bracket because the battery pack has strap loops, the top strap removed, a no-stretch strap added to support that battery and keep the main strap off my ears, the front bracket flipped to provide a better bracing angle against the head and padded with extra strap material, the battery pack not quite centered to keep it off the center bump on the back of my head:
Others do the mixed TIR thing with dual emitters, like the the LEDX Kaa 2000, Lucifer Lights M6 and S2X, etc. I haven't tried those lights, but I know that gives the kind of beam profile that I like.
Here's me running with the predecessor of my Yinding, a Gemini Duo (replaced by much cheaper Yinding after driver failed after 3 years). Note that I wear the headlamp as high as possible on my head, which I find best for stability and better separation of the light from my eyes for more shadow definition. I dropped a 4:46 downhill mile down a dark trail in middle of a 50 mile race immediately after this photo was taken. I've also topped other downhill trail Strava segments at faster than 4:50 per mile pace for 2+ miles in the dark with the Yinding or Gemini headlamps on high at 1200 lumens.
I'm not quite satisfied with this headlamp. I am kind of a CRI and warm emitter snob, since I think those improve vision out in the woods. There are no good high CRI warm emitters in the XM-size to modify my Yinding, so I've been looking into other things.
For instance, a quad flashlight with Nichia E21A emitters (I'd go for the 2700K) and the frosted Carclo optics look like they have a great beam profile in the following reddit post. I'd be willing to try strapping a flashlight to my head with a similar setup to the reddit post, but I can't say how well it works for running until I actually try it. Also, the single 18650 battery is only good for not quite 1.5 hours at around 400 lumens, so more like a short run or backup solution for me (runtime estimated from this review:
https://zeroair.org/2020/10/30/emisar-d4v2-brass-with-e21a-emitters-flashlight-review/ ) :
https://www.reddit.com/r/flashlight...band_d4v2_e21a_3500k_awesome_cri_98_headlamp/